Match the columns :

	Column I		Column II
a)	$\underset{n\to \infty }{Lim}\left[{\int }_0^2\frac{{(1+\frac{t}{n+1})}^n}{n+1}dt\right]$  is equal to	p)	$e-\frac{1}{2}{e}^2-\frac{3}{2}$
b)	Let f(x) be a function satisfying  $f\text{'}\left(x\right)=f\left(x\right)$  with f (0) = 1 and g be the function satisfying  $f\left(x\right)+g\left(x\right)=x^2$. Then the value of the integral  ${\int }_0^{1}f\left(x\right)g\left(x\right)dx$ is	q)	$e^2$
c)	${\int }_0^1{e}^{e^x}(1+x{e}^x)dx$ is equal to	r)	$e^2-1$
d)	$\underset{k\to 0}{\lim }\frac{{\displaystyle {\int }_0^k{(1+\sin 2x)}^{1/x}dx}}{k}$	s)	$e^e$